A Matter of Probability
by TayteFFN
Summary: Hector&Eliwood are fighting a Hydra. Hector has a 60% chance of beheading 1 head, Eliwood 30%, together 20%  they get in each other's way . If 1 attack can be followed by another to eliminate 2 of the heads, what is the optimal method of attack?


**A/N: This is what I did when I should have been studying for AP Stats.**

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><p>When I said friendship between fugitives, I hadn't taken into account that I would be required to help him win the love of his life. Poor kid. I knew he had principles, but I didn't realize he still believed in true love. Alas, I wanted a wyvern knight watching my back, so the least I could have been able to do was help him woo his woman. That's what I thought when I agreed. But don't get too far ahead, my friend, for when I say woo his woman, you've got to understand the definition of "his woman."<p>

By "his woman," I mean the tactician, Natalia. Natalia was a woman of wits. Yes, I know, _duh _as you young folk like to say these days. She was not particularly beautiful like Isadora, but she did the whole army's finances in her head while we traveled from one place to another and spouted off how to stock up for the next battle like she was spouting off the ABCs. She liked her food spicy and didn't like poetry and wasn't known to be very humble, which is what caused the whole problem in the first place. What all this meant, however, was that impressing her was no small feat, because not only did she care little for flowers, we found out the hard way she had different ideas of what jewelry meant as well. Maybe I should just start here.

It all began back at the Water Temple. That was a bad time. We had gone after Nino and Jaffar to give Sonia a visit and, well, hell happened. But believe me, that stuff's not even close to interesting compared to this. Natalia had sent Heath and me over to this random island of treasure chests (she shared my philosophy of reallocating resources) and I barely had enough time to remove the ring from the last chest before I hurled Lowen's beef stew where the ring used to be. (I never did get used to the hair-raising dives and neck-wrenching turns of a wyvern.) Heath must have thought the ring looked pretty good, because he snatched it out of my hand and promptly announced, "Iwill hand her this one."

The custom was that all reallocated items be given to Natalia ASAP so she could then re-reallocate them properly. It was three in the morning and I had managed to get a wink or two of sleep while Heath flew the wyvern back to Natalia, so I have a distinct memory of her hollering at Sain to ditch his horse and swim back to land because he needed to protect Ninian. I can't say for a fact that last part happened, but I do remember crystal clear what happened in the exchange between Natalia and Heath.

Natalia was in the state of tearing out her blonde hair at that moment. I noticed this mostly because her jewel-encrusted blue headband had popped off and rested at her feet, not to be missed ever again (because I notice things like that). She was expressing her frustration in a particular noise that sounded like a pegasus hiccupping in the middle of a sneeze, but stopped when Raven looked back to make sure she hadn't been beheaded by a misplaced hand axe via Dart or something. Natalia cleared her throat and brushed her cloak out like a gentlewoman and smiled to see Heath and me landing.

Naturally, I leapt (fell) off the scaly beast and showed her the fruits of my efforts, and she looked much pleased for about five seconds.

"Heath, what are you doing?" she asked, alarmed to see him clumsily clambering down from his perch.

He cleared his throat and looked at me once (probably expecting some encouraging nod or something, which he didn't receive) and answered her concern.

"There was something more we found," he said, and he took her hand quickly and shoved the ring into it. I would have said "How bold" that he took her hand, but he let go so quickly it was as if he was afraid of getting cooties.

"I thought," he said, "that it would suit you well."

Natalia's eyes lit up. If this was a Lycian drama, all of the lights would have gone down to accentuate her glowing face as she turned to grant her knight a kiss, a simple peck, a mere tease of what might come. But this is not a Lycian drama, so she swiftly turned tail and hurried off in Ninian's general direction, leaving me to stand in awkward silence with my fugitive friend and Raven to curse and run after the tactician (it was apparently his turn to protect her).

"So," I said. "What are we on, Plan Q now?"

Heath glared at me.

Twenty minutes later, I don't remember where Heath was, but I was hiding behind Sain's malodorous, wet horse, listening to Ninian explain the significance of the ring to Natalia.

"Thor's Ire," said Ninian, "will raise the chance of successfully striking the enemy to nearly a guarantee."

"Could have been useful back when we were fighting Uhai," said Natalia, always the optimist.

"My fair lady!" exclaimed Sain from atop his stinky horse. "Be glad, for I had cast him aside for your smile! Tell me how I may service you further! What would you have me do next?"

"Nothing, Sain," Natalia replied through gritted teeth. "Now that you are going to die of pneumonia, you don't need to ever do anything ever again." And then she smiled. It was a well-known fact that Natalia had nursed a deep hatred of Sain since the day the two met. Sain just…never realized it.

"Oh, but I would not leave you so broken-hearted, my love!" replied Sain…or, well he said something along those lines. "I loan you my strength as I do my love, forevermore do I swear!"

"You swear?" Now there was a glint in Natalia's eye. "Why, Sain, there _is _something I would like you to do for me. Let's make a wager."

"What's this? Gambling, my lady?"

"Call it what you like," she replied. "For you, I like to call it a challenge. Listen carefully, because I am only saying it once."

"And the stakes are?"

"If you can solve this riddle in seven days," Natalia crossed her arms, "I shall give you one kiss."

"…And the alternative?"

"You cease flirting with me forever."

Sain frowned and was silent for a full two minutes. Seemed like a truly terrible choice, judging by the painfully exaggerated thinking poses Sain put himself in as we all proceeded our way towards the center of the Water Temple, dodging the occasional Bolt (courtesy Sonia) and generally pummeling through whatever morphs came our way (courtesy Raven).

"I accept your challenge."

"By the way, if you receive help of any sorts, the kiss will go to someone else instead."

"What! That wasn't part of the agreem—!"

"Hector and Eliwood, armed with Armads and Durandal, are fighting a Hydra. Alone, Hector has a 60% chance of beheading one head whereas Eliwood has a 30% chance. Together, because they get in each other's way, they only have a 20% of successfully beheading two heads. If one attack can be followed by another in an attempt to eliminate two of the hydra's heads, how do we optimize the method of attack? You have one chance to answer with a complete reasoning."

Sain was quiet. Raven was quiet. Ninian was quiet. Somewhere far away, Jaffar was helping Sonia commit assisted seppuku. As Natalia led Sain and Raven into the brunt of armor-less (and shirtless) brutes with axes, Ninian turned to me and said, "This is not going to end well."

I wasn't paying attention. Heath now had a Plan Q.

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><p><strong>It's an Algebra II probability problem really. Think you can solve it?<strong>


End file.
